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These are questions asked by DJJerome1976

I am working with lines in 2- and 3-space, defined parametrically. In 2-space, how would I go about using Maple to determine if the lines are identical or parallel. For example, if L1:=<2-4*t,5+6*t>, L2:=<-6-12t,17+18t>, L3:=<20t,-30t>, I would like a procedure that would be able to determine that L1 and L2 are identical lines, and that L1 and L3 are parallel lines. Similarly, it would be able to determine if lines in 3-space, are identical, parallel, or skew. 


I was looking into the geometry package, but I don't think it allows me to do this.



I am trying to check to see if two equations are equivalent, subject to rearrangment and scalar multiplication. For example, I would to have a procedure that would determine that each of the following equations are the equivalent:

(a) (1/2)*y*exp(-y)+2*y^3 - x*ln(x) +x^2 = 10
(b) (1/2)*y*exp(-y)+2*y^3 +x^2 = 10 + x*ln(x)

(c) y*exp(-y)+4*y^3 - 2*x*ln(x) +2*x^2 = 20

Is there a systematic way to go about doing this? Thanks!

I'm doing some work with undirected and directed graphs, and I'm needing to find examples of longest paths and longest cycles.  How may this be done in Maple?


I am using A:=LinearAlgebra:-RandomMatrix(10,10,generator=-10..10) to generate a random matrix. How may I specify that every row of A has at least three non-zero entries? 


I am playing around with certain "simple" integrals, and came across this strange behavior in Maple. Maple is able to integrate sin(x)^(1/2)*cos(x)^3, but not sin(x)^(1/3)*cos(x)^3. Any idea why?

int(sin(x)^(1/2)*cos(x)^3, x)



int(sin(x)^(1/3)*cos(x)^3, x)

int(sin(x)^(1/3)*cos(x)^3, x)



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